A small electric dipole p _0, having a moment of inertia I about its center, is kept at a distance r from the center of a spherical shell of radius R. The surface charge density is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle as shown in the figure.

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A small electric dipole p _0, having a moment of inertia I about its center, is kept at a distance r from the center of a spherical shell of radius R. The surface charge density is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle as shown in the figure. While staying at a distance r, the dipole is free to rotate about its center. If released from rest, then which of the following statement(s) is(are) correct? [ _0 is the permittivity of free space.]

Quantrex Academy · Accepted Answer

Correct answer: D. The dipole will undergo small oscillations with an angular frequency of p_0 100 _0 I at r=10 R.

$ aligned & =| p E | \ & I =p_0 E \ & = p I ( 1 4 _0 4 R^2 r^2 ) \ & = ( p 0 R^2 I _0 r^2 ) \ & = p 0 R^2 I _0 r^2 aligned $ For $r=2 R$ $ = p_0 4 / _0 ( C $ is incorrect $)$ Also, for $r=10 R$ $ = p_0 4 l(100) $ (D is correct) It will oscillate for any finite value of $r>R$. (B is correct)

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